Many instructors will teach that the proper tool for back kick is the heel, and then modify the heel to the footsword as the student improves in ability and understanding. The footsword near the heel is the proper tool for a back kick - but there are people who were taught heel for various reasons (translation errors, miscomprehension, poor explanations, etc.) who then passed on heel to their own students.
While many people teach side kick as a forward turn (keeping the eyes on the target), and back kick as a rearward turn (turning the back to the target before reacquiring the target after the head turns), that is a simplification for junior students who are just learning the two kicks. In a back kick, the hips are square to the target; in a side kick, the hips are turned slightly toward the target; both kicks use the footsword as the tool.
I will qualify this, however, by saying that other styles teach side kick differently than we do, with the kicking foot being parallel to the floor; we teach it with the kicking foot perpendicular to the floor (heel pointing to the ceiling, toes pointing at the floor); later we teach side kick with the foot parallel to the floor as a variation on the basic perpendicular foot position. For people who teach the foot parallel position as the primary form of the kick, terrylamar's description is correct.
This is, of course, one of the basic problems with such questions: different styles, different organizations, even different schools may have a different interpretation of even basic techniques, so that multiple explanations can be equally true.
